Recall That the Total Income Received from Time $t = a$

Multiple Choice

Recall that the total income received from time $t = a$ to time $t = b$ from a continuous income stream of $R ( t )$ dollars per year is
Total value = TV = $\int _ { a } ^ { b } R ( t ) \mathrm { d } t$
Find the total value of the given income stream and also find its future value (at the end of the given interval) using the given interest rate.
$R ( t ) = 800,000 \sin ( 2 \pi t )$ , $0 \leq t \leq 5$ , at 9%

A) TV = $0, FV = $72,344.91
B) TV = $0, FV = $327,074.77
C) TV = $1,600,000, FV = $834,722.23
D) TV = $0, FV = $256,372.45
E) none of these